CHARACTERIZATION OF PIEZOELECTRIC CERAMIC MATERIALS
T. L. J ORDAN
Z. OUNAIES
NASA Langley Research Center Hampton, VA
INTRODUCTION
This article explores piezoelectric ceramics analysis and characterization. The focus is on polycrystalline ceramics;
therefore, single crystals, polymeric materials, and or- ganic /inorganic composites are outside the scope of this review. To grasp the behavior of a piezoelectric polycrys- talline ceramic thoroughly, a basic understanding of the ceramic itself should not be overlooked. To this end, we have presented a brief introduction of the history of piezo- electricity and a discussion on processing of the ceramic and the development of the constitutive relationships that define the behavior of a piezoelectric material. We have at- tempted to cover the most common measurement methods and to introduce parameters of interest. Excellent sources for more in-depth coverage of specific topics can be found in the bibliography. In most cases, we refer to lead zirconate titanate (PZT) to illustrate some of the concepts because it is the most widely used and studied piezoelectric ceramic to date.
PIEZOELECTRIC MATERIALS: HISTORY AND PROCESSING
Smart materials are materials that undergo transforma- tions through physical interactions. An alternate definition is that a smart material is a material that senses a change in its environment and adapts to correct or eliminate such a change by using a feedback system. Piezoelectric materi- als, shape-memory alloys, electrostrictive materials, mag- netostrictive materials, and electrorheological fluids are some examples of currently available smart materials.
Piezoelectricity stems from the Greek word piezo for pressure. It follows that a piezoelectric material develops a
potential across its boundaries when subjected to a mecha- nical stress (or pressure), and vice versa, when an electric field is applied to the material, a mechanical deformation ensues. Therefore, piezoelectric materials fall in the class of smart materials. Ferroelectricity is a subgroup of piezo- electricity, where a spontaneous polarization exists that can be reoriented by applying an ac electric field.
Definition and History
Piezoelectricity is a linear effect that is related to the mi- croscopic structure of a solid. Some ceramic materials be- come electrically polarized when they are strained; this linear and reversible phenomenon is referred to asthe di- rect piezoelectric effect. The direct piezoelectric effect is al- ways accompanied bythe converse piezoelectric effectwhere a solid becomes strained when placed in an electric field.
The microscopic origin of the piezoelectric effect is the displacement of ionic charges within a crystal structure.
In the absence of external strain, the charge distribution within the crystal is symmetrical, and the net electric dipole moment is zero. However when an external stress is applied, the charges are displaced, and the charge distribu- tion is no longer symmetrical. A net polarization develops and results in an internal electric field. A material can be piezoelectric only if the unit cell has no center of inversion.
Piezoelectricity is a property of a group of materials that was discovered in 1880 by Pierre and Jacques Curie dur- ing their study of the effects of pressure on the generation of electrical charge by crystals such as quartz, tourmaline, and Rochelle salt. In 1881, the term “piezoelectricity” was first suggested by W. Hankel, and the converse effect was deduced by Lipmann from thermodynamics principles. In the next three decades, collaborations within the European scientific community established the field of piezoelectri- city, and by 1910, Voigt’sLerbuch der Kristallphysicwas published and became a standard reference work detail- ing the complex electromechanical relationships in piezo- electric crystals (1). However, the complexity of the science of piezoelectricity made it difficult for it to mature to an application until a few years later. Langevin et al. (2) de- veloped a piezoelectric ultrasonic tranducer during World War I. Its success opened up opportunities for piezoelectric materials in underwater applications and a host of other applications such as ultrasonic transducers, microphones, and accelerometers. In 1935, Busch and Scherrer disco- vered piezoelectricity in potassium dihydrogen phosphate (KDP). The KDP family was the first major family of piezo- electrics and ferroelectrics discovered.
During World War II, research in piezoelectric materi- als expanded to the United State, the Soviet Union, and Japan. Until then, limited performance by these materi- als inhibited commercialization, but that changed when a major breakthrough came with the discovery of barium ti- tanate and lead zirconate titanate (PZT) in the 1940s and 1950s, respectively. These families of materials exhibited very high dielectric and piezoelectric properties. Further- more, they offered the possibility of tailoring their behavior to specific responses and applications by using dopants.
To date, PZT is one of the most widely used piezoelec- tric materials. Most commercially available ceramics (such
CHARACTERIZATION OF PIEZOELECTRIC CERAMIC MATERIALS 163
Pb
O
Ti, Zr
Figure 1. Perovskite structure.
as barium titanate and PZT) are based on the perovskite structure (Fig. 1). The perovskite structure (ABO3) is the simplest arrangement where the corner-sharing oxy- gen octahedra are linked together in a regular cubic array; smaller cations (Ti, Zr, Sn, Nb, etc.) occupy the central octahedral B site, and larger cations (Pb, Ba, Sr, Ca, Na, etc.) fill the interstices beween octahedra in the larger A site. Compounds such as BaTiO3, PbTiO3, PbZrO3, NaNbO3, and KNbO3 have been studied at length and their high-temperature ferroelectric and antiferroelectric phases have been extensively exploited. This structure also allows multiple substitutions at the A site and B site that result in a number of useful though more complex com- pounds such as (Ba,Sr)TiO3, (Pb,Sr)(Zr,Ti)O3, Pb(Fe,Ta)O3, and (KBi)TiO3.
Starting around 1965, several Japanese companies fo- cused on developing new processes and applications and opening new commercial markets for piezoelectric devices.
The success of the Japanese effort attracted other nations, and today the needs and uses extend from medical applica- tions to the communications field to military applications and the automotive field.
A review of the early history of piezoelectricity is found in the work of Cady (3), and in 1971, Jaffe et al. published the bookPiezoelectric Ceramics(4) that is still one of the most referenced works on piezoelectricity.
Piezoelectric Ceramic Processing
The fabrication of most bulk piezoelectric ceramics starts with powder preparation. The powder is then pressed to the required shapes and sizes, and the green shapes are in turn processed into mechanically strong and dense ce- ramics. The more important processes that influence the product characteristics and properties are powder prepa- ration, powder calcining and sintering. The next steps are machining, electroding, and poling, the application of a dc field to orient the dipoles and induce piezoelectricity.
The most common powder preparation is the mixed- oxide. In this process, powder is prepared from the ap- propriate stoichiometric mixture of the constituent oxides.
Lead oxide, titanium oxide, and zirconium oxide are the main compounds for, lead zirconate titanate (PZT). De- pending on the application, various dopants are used to tai- lor the properties of interest. PZT ceramics are rarely used
Wet milling Zirconia media + Ethanol
24 hrs
Drying at 80°C, 12 hrs Sieving for better mixing and
size reduction
Ready for calcining PbO, TiO2, ZrO2 dopants if needed Mixing of oxides:
Figure 2. Mixed-oxide route for preparing PZT.
without adding of dopants to modify some of their proper- ties. A-site additives tend to lower the dissipation factor, which affects heat generation, but also lower the piezo- electric coefficients; for this reason they are used mostly in ultrasonics and other high-frequency applications. B-site dopants increase the piezoelectric coefficients but also in- crease the dielectric constant and loss. B-site doped ceram- ics used are as actuators in vibrational and noise control, benders, and optical positioning applications.
Figure 2 shows a flowchart of the mixed-oxide route for making PZT ceramics. The powders can be mixed by dry ball milling or wet ball milling; both methods have advan- tages and disadvantages: wet ball milling is faster than dry milling; however, the disadvantage is the added step of liquid removal. The most common method for making PZT ceramics is wet ball milling; ethanol and stabilized zirconia media are added for wet milling. A vibratory mill may be used rather than a conventional ball mill; Herner (5) showed that this process reduces the risk of contamina- tion by the balls and the jar. Zirconia media are used to re- duce the contamination risks further. Calcination is a very crucial step in processing PZT ceramics; it is important for crystallization to be complete because the perovskite phase forms during this step. The goals are to remove any organics, water, or other volatiles left after mixing; to re- act the oxides to form the desired phase composition before the ceramic is processed into useful devices; and to reduce volume shrinkage and allow for better homogeneity during and after sintering.
After calcining, a binder is added to the powder, and then the mixture is shaped usually by dry pressing in a die for simple shapes, or extrusion, or casting for more compli- cated bodies. Next, the shapes are sintered—placed in an oven for binder burnout and densification.
164 CHARACTERIZATION OF PIEZOELECTRIC CERAMIC MATERIALS The major problem in sintering a PZT ceramic is the volatility of PbO at about 800◦C. To minimize this prob- lem, the PZT samples are sintered in the presence of a lead source, such as PbZrO3, and placed in closed crucibles. Sat- uration of the sintering atmosphere with PbO minimizes lead loss from the PZT bodies. Sintering can now be car- ried out at temperatures varying between 1200–1300◦C.
Despite precautions, usually 2–3% of the initial lead con- tent is lost.
After cutting and machining into desired shapes, elec- trodes are applied, and a strong dc field is used to orient the domains in the polycrystalline ceramic. Dc poling can be done at room temperature or at higher temperatures, depending on the material and the composition. The poling process only partially aligns the dipoles in a polycrystalline ceramic, and the resulting polarization is lower than that of single crystals.
This processing technique presents many uncertainties;
the existence of a wide number of other fabrication tech- niques is an indication that there is a great need for the production of reliable PZT ceramics whose properties and microstructure are optimal. One problem often encoun- tered is deviation from stoichiometry. This problem is often due to impurities in the raw materials as well as the lead loss during sintering, and invariably results in substantial alterations of the PZT properties. As a result, the elas- tic properties can vary as much as 5%, the piezoelectric properties 10%, and the dielectric properties 20% within the same batch (6). The piezoelectric and dielectric prop- erties generally suffer also if there is any lack of homo- geneity from poor mixing. It is important then that the constituent oxides be intimately mixed. In the method de- scribed before, however, the constituents are solid solutions and it has been shown that intimate mixing of solid so- lutions is difficult if not impossible. More information on the preparation of piezoelectric ceramics can be found in Jaffe et al. (4), and Moulson and Herbert (7). Other pro- cessing methods, including hydrothermal processing and coprecipitation methods, are described in (8–10). Noted that there has been a great deal of development in pow- der processing, shaping, and sintering (11–13) that has re- sulted in further expanding the application of piezoelectric ceramics.
Ferroelectricity
Some piezoelectric materials are also ferroelectric. A fer- roelectric material possesses spontaneous polarization whose direction can be reversed by applying a realiz- able electric field across some temperature range. Most ferroelectric materials have a Curie temperature Tc be- low which they are polar and above which they are not.
The dielectric permittivity often has a peak atTcand lin- early decreases above it according to the Curie–Weiss law (4,7). The very large permittivity values that are charac- teristic of ferroelectric materials are greatly exploited in many applications, most widely in the multilayer-capacitor industry.
Applying a large alternating electric field reverses the polarization, and this gives rise to the ferroelectric
Pr
Ec
Polarization
Electric field
Figure 3. P–E hysteresis loop of a poled piezoelectric ceramic.
hysteretic loop that relates polarization Pto applied elec- tric field E. A typical field-polarization loop is illustrated in Fig. 3. For large signals, both the electric displacement D and the polarization P are nonlinear functions of the fieldE. They are related to each other through the linear equation
Di=Pi+ε0Ei, (1) whereε0 is the permittivity of free space (=8.85×10−12 C/ Vm). The second term in Eq. (1) is negligible for most ferroelectric ceramics, and a D–Eloop and P–Eloop be- come interchangeable. Two key characteristics of theP–E loop are the coercive fieldEcand the remanent polarization Pr, both defined by analogy to ferromagnetic materials.Ec
is the field at which polarization is zero.Pris the value of the polarization when the electric field is zero. Once the field is switched off, the material’s polarization is equal to Pr. Once the P–Eloop is saturated, bothPrand Eccan be determined. A loop is said to be saturated once the values ofPrandEcno longer vary.
Generally, the existence of the P–Eloop is considered evidence toward establishing that a material is ferroelec- tric. A Sawyer–Tower circuit (14), or a modified version of it, is commonly used to obtain aP–Eloop. An ac voltage is applied to the electroded sample; the resulting charge stored on the sample is determined by a large reference capacitor placed in series with the sample. An electrome- ter can be used to detect the voltage across the capacitor; by multiplying this voltage by the value of the reference capac- itor, the charge across the sample results. The capacitance of the reference capacitor should be 100 to 1000 times the value of the capacitance of the sample. Note that ferroelec- tric hysteretic loops are both frequency- and temperature- dependent.
In addition to theP–Eloop, polarization switching leads to strain–electric field hysteresis. A typical strain–field
CHARACTERIZATION OF PIEZOELECTRIC CERAMIC MATERIALS 165
Strain
Electric field
Figure 4. Butterfly loop indicating switching.
response curve is shown in Fig. 4. The shape resembles that of a butterfly, and it is often referred to as the “but- terfly loop.” As the electric field is applied, the converse piezoelectric effect dictates that a strain results. As the field is increased, the strain is no longer linear with the field, as domain walls start switching.
For more sources on ferroelectricity, the reader should consult the bibliography (15–19).
PIEZOELECTRIC CONSTITUTIVE RELATIONSHIPS
An understanding of piezoelectricity begins with the struc- ture of the material. To explain it better, let us consider a single crystallite (a small single crystal less than 100µm in average diameter) from a polycrystalline ceramic. This crystal is made up of negatively and positively charged atoms that occupy specific positions in a repeating unit or cell. The specific symmetry of the unit cell determines the possibility of piezoelectricity in the crystal. All crystals can be divided into 32 classes or point groups (from seven basic crystal systems: triclinic, monoclinic, orthorhombic, tetragonal, rhombohedral, hexagonal, and cubic). Of the 32 classes, 21 do not possess a center of symmetry, and 20 are piezoelectric (although one class lacks a center of sym- metry, it is not piezoelectric because of the combination of other symmetry elements). The lack of a center of symme- try means that a net movement of positive and negative ions with respect to each other as a result of stress pro- duces an electric dipole. Because the ceramic is composed of randomly oriented piezoelectric crystallites, it is inac- tive, that is, the effects of the individual crystals cancel each other and no discernable piezoelectricity is present.
Regions of equally oriented polarization vectors are known as domains. “Poling” is a commonly used method to orient the domains by polarizing the ceramic through the appli- cation of a static electric field. Electrodes are applied to
V= 0 V= n
Figure 5. Poling of a piezoelectric, ferroelectric ceramic.
the ceramic, and a sufficiently high electric field is applied such that the domains rotate and switch in the direction of the electric field. Full orientation of all domains never re- sults; however, the polycrystalline ceramic exhibits a large piezoelectric effect. During this process, there is a small expansion of the material along the poling axis and a con- traction in both directions perpendicular to it (see Fig. 5).
Due to large number of allowable polar directions such as near the morphotropic phase boundary (where the Zr to Ti ratio is 48 to 52), the maximum deviation of the polar axis of a grain from the average polar direction is smaller, and the reduction of polarization is minimized, assuming optimum alignment.
Constitutive Relationships
When writing the constitutive equations for a piezoelec- tric material, account must be taken of changes of strain and electrical displacement in three orthogonal directions caused by cross-coupling effects due to applied electrical and mechanical stresses. Tensor notation is first adopted, and the reference axes are shown in Fig. 6. The state of strain is described by a second-rank tensor Si j, and the state of stress is also described by a second-rank tensor Tkl. The relationships relating the stress tensor to the strain tensor, compliancesi jkl, and stiffnessci jkl, are then fourth-rank tensors. The relationship between the electric field Ej(first-rank tensor) and the electric displacement Di(also a first-rank tensor) is the permittivity εi j, which is a second-rank tensor. Therefore the piezoelectric
3 6
4 1
5 2
Figure 6. Reference axes.
166 CHARACTERIZATION OF PIEZOELECTRIC CERAMIC MATERIALS
equations are
Di=εi jTEj+di jkTjk, (2)
Si j=di jkEk+si jklE Tkl, (3)
wheredi jk,di jkare the piezoelectric constants (third-rank tensor). SuperscriptsTand Eindicate that the dielectric constant εi j and the elastic constant si jkl are measured under conditions of constant stress and constant electric field, respectively. In general, a first-rank tensor has three components, a second-rank tensor has nine components, a third-rank tensor has 27 components, and a fourth-rank tensor has 81 components. Not all of the tensor components are independent.
Both of these relationships depend on orientation; they describe a set of equations that relate these properties in different orientations of the material. The crystal symme- try and the choice of reference axes reduce the number of independent components. A convenient way of describ- ing them is by using axis directions, as given by Fig. 6.
The convention is to define the poling direction as the 3 axis, the shear planes are indicated by the subscripts 4, 5, and 6 and are perpendicular to directions 1, 2, and 3, respectively. This simplifies the notations introduced be- fore, where a 3-subscript tensor notation (i,j,k=1,2,3) is replaced by a 2-subscript matrix notation (i=1,2,3 and j=1,2,3,4,5,6), and a 2-subscript tensor notation (i,j=1,2,3) is replaced by a 1-subscript matrix notation (i=1,2,3,4,5,6). A shear strain such asS4is a measure of the change of angle between the two initially orthog- onal axes in the plane perpendicular to axis 1. The first subscript of thedconstant gives the “electrical” direction (field or dielectric displacement), and the second gives the component of mechanical deformation or stress. The pla- nar isotropy of poled ceramics is expressed in their piezo- electric constants by the equalities d32=d31 (an electric field parallel to the poling axis 3 interacts in the same way with axial stress along either the 2 axis or the 1 axis) and d24=d15(an electric field parallel to the 2 axis interacts in the same way with a shear in the 2,3 plane as a field along the 1 axis with a shear in the 1,3 plane). Similar relation- ships hold for the elastic constants because of isotropy in the plane perpendicular to the polar axis.
Property Matrix for a Poled Piezoelectric Ceramic
A piezoelectric ceramic has only one type of piezoelectric matrix, regardless of the symmetry of the constituent crys- tals. The ceramic is initially isotropic. This isotropy is destroyed in the poling direction. The material is trans- versely isotropic in the directions perpendicular to the pol- ing direction. The symmetry elements are an axis of ro- tation of infinite order in the direction of poling and an infinite set of planes parallel to the polar axis as reflection planes. In crystallographic notation, this symmetry is de- scribed as∞mmand is equivalent to the hexagonal polar crystal class, 6 mm.
The elastic, dielectric, and piezoelectric matrices for the cylindrical symmetry of poled PZT are shown in the follow- ing equations. Matrices analogous to the piezoelectric also apply to other piezoelectric constants such asgi j(described
in the next section).
s11 s12 s13 0 0 0 s12 s11 s13 0 0 0 s13 s13 s33 0 0 0
0 0 0 s44 0 0
0 0 0 0 s44 0
0 0 0 0 0 2(s11−s12)
(4)
ε1 0 0 0 ε1 0 0 0 ε3
(5)
0 0 0 0 d15 0
0 0 0 d15 0 0
d31 d31 d33 0 0 0
(6)
For the symmetry of poled ceramics then, general Equa- tions (1) and (2) are replaced by the these specific equations:
D1=ε1E1+d15T5, (7) D2=ε2E2+d15T4, (8) D3=ε3E3+d31(T1+T2)+d33T3, (9) S1=s11ET1+s12ET2+s13ET3+d31E3, (10) S2=s11ET2+s12ET1+s13ET3+d31E3, (11) S3=s13E(T1+T2)+s33ET3+d33E3, (12) S4=s44ET4+d15E2, (13) S5=s44ET5+d15E1, (14)
S6=s66ET6. (15)
Equations (7)–(9) relate to the direct effect, and Eqs. (10)–
(15) relate to the converse effect.
PIEZOELECTRIC PARAMETERS: DEFINITIONS AND CHARACTERIZATION
The parameters that are of interest when considering the electromechanical effects of piezoelectric materials are the piezoelectric charge coefficients (d31andd33), the piezoelec- tric voltage coefficients (g31andg33), and the piezoelectric coupling factors (k31,k33,kp, and kt). The dcoefficient is the proportionality constant between electric displacement and stress, or strain and electric field [Eqs. (2) and (3)].
Highdcoefficients are desirable in materials used as actu- ators, such as in motional and vibrational applications. The gcoefficient is related to thedcoefficient by the following expression:
dmi=εTn mgni. (16) where m,n=1,2,3 and i=1,2, . . .6. High gcoefficients are desirable in materials to be used as sensors to produce voltage in response to mechanical stress.
The piezoelectric coupling factorkis a measurement of the overall strength of the electromechanical effect. It is often defined as the square root of the ratio of electrical